On the use of simulated annealing method and cross-validation theory for deconvolution of seismograms

In order to retrieve the apparent source time function (ASTF) seen at a given station, one must take into account propagation effects, site, and instrumental influences. Removing these effects can be performed by a deconvolution of the mainshock seismogram by a seismogram of a smaller event recorded at the same station. This smaller event must occur nearby the mainshock, and the associated seismogram is considered as an empirical Green's function. We propose a deconvolution based on the simulated annealing method, and we compare it with the often-used spectral division technique. We show on both synthetic and real signals that the simulated annealing deconvolution (SAD) provides stable and positive ASTF, whereas results from spectral division are very sensitive to an ad hoc parameter called water level. Finally, the application of cross-validation analysis between the three components of the seismogram in addition to the (SAD allows us to estimate errors on the ASTF.